Depending on your state laws:
You don't do the drilling - IME the bank hires a professional locksmith to come in and "drill" the box to get it open - in your presence and in the presence of the bank officer.
Now, here in Florida, we are authorized to do safe deposit box inventories and sign off on it; is this an authorized notarial act in your state? (You don't say where you're from). Your notary laws may not authorize you to take the inventory, but they MAY authorize you to notarize the signature of the bank officer that does. If you are authorized to do this, you watch them open it, inventory each item (listing on a form usually provided by the bank) and either you sign the inventory or the officer does and you notarize their signature. Then, here in FL, the contents are put in a bag and sealed with the list on the inside and outside - and kept by the bank.
These jobs can be quick (if the box is empty) - however if the box has items in it, it can be more time-consuming depending on how full it is - each item must be individually listed. So if you're able to do these under your laws make sure you keep your fee open-ended - $xx amount if empty, possibly more if time required to itemize inventory.